The area of the triangle formed by points of intersection of parabola y=a(x-3)(x+2) with the coordinate axes is 10. The constant (a) of the function is 4.
The triangle formed by the parabola has a base equal to the distance between the points where the graph touches the x-axis and height (h) is the point where the graph touches the y-axis.
The points on the x-axis are the roots of the quadratic equation:
a(x-3)(x+2)=0
(x-3)(x+2)=0
x - 3 = 0
x = 3
or
x + 2 = 0
x = -2
So, the base is the distance between (-2,0) and (3,0).
Since they are in the same coordinate, the distance here;
b = 3 - (-2)
b = 5
The area of the triangle is 10. So
5a = 10 x 2
a = 4
The constant (a) of the function y = a(x-3)(x+2) is 4.
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